We modified CLASS v3.1 [1]} to include the stepped fluid [2]} and further modified the code to include interactions with DM as described in Appendix .
We use the MontePython v3.5 [3]}, [4]} MCMC sampler to study the constraints of various data sets on the model.
Similar to Ref. [2]}, for the WZDR+ model, we adopt flat priors on the 6 \(\Lambda {\rm CDM}\)  cosmological parameters \(\lbrace \omega _b,\, \omega _{\rm dm},\, \theta _s, n_s, A_s,\, \tau _{\rm reio} \rbrace \) . For the 3 new parameters of WZDR+ we include a flat prior on the amount of dark radiation after the stepThe lower bound was included to avoid numerical issues of our code near \(N_\text{IR}=0\) . We explicitly checked that our results are not very sensitive to small changes of this bound. \(N_\text{IR}> 0.01\) , a logarithmic prior on the redshift of the step locationThese bounds are designed to avoid scanning over models in which the transition occurs too early or too late to have much effect on the CMB, see [2]}. \(\log _{10} (z_t) \in [4.0, 4.6]\) , and a linear prior on the strength of the interaction between dark radiation and dark matter \(\Gamma _0>0\) .
